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Projection methods for conic feasibility problems; applications to sum-of-squares decompositions

Didier Henrion 1 Jérôme Malick 2
1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes
2 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
Abstract : This paper presents a projection-based approach for solving conic feasibility problems. To find a point in the intersection of a cone and an affine subspace, we simply project a point onto this intersection. This projection is computed by dual algorithms operating a sequence of projections onto the cone, and generalizing the alternating pro jection method. We release an easy-to-use Matlab package implementing an elementary dual projection algorithm. Numerical experiments show that, for solving some semidefinite feasibility problems, the package is competitive with sophisticated conic programming software. We also provide a particular treatment of semidefinite feasibility problems modeling polynomial sum-of-squares decomposition problems.
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Submitted on : Thursday, May 28, 2009 - 7:55:38 PM
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Didier Henrion, Jérôme Malick. Projection methods for conic feasibility problems; applications to sum-of-squares decompositions. Optimization Methods and Software, Taylor & Francis, 2009, 26 (1), p. 23-46. ⟨inria-00389553⟩

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